One way a difference tone can be heard is when two tones with fairly complete sets of harmonics make a just fifth. This can be explained as an example of the missing fundamental phenomenon. If is the missing fundamental frequency, then would be the frequency of the lower tone, and its harmonics would be etc. Since a fifth corresponds to a frequency ratio of 2:3, the higher tone and its harmonics would then be etc. When both tones are sounded, there are components with frequencies of etc. The missing fundamental is heard because so many of these components refer to it.
The specific phenomenon that Tartini discovered was physical. Sum and difference tones are thought to be caused sometimes by the non-linearity of the inner ear. This causes intermodulation distortion of the various frequencies which enter the ear. They are combined linearly, generating relatively faint components with frequencies equal to the sums and differences of whole multiples of the original frequencies. Any components which are heard are usually lower, with the most commonly heard frequency being just the difference tone, , though this may be a consequence of the other phenomena. Although much less common, the following frequencies may also be heard:
For a time it was thought that the inner ear was solely responsible whenever a sum or difference tone was heard. However, experiments show evidence that even when using headphones providing a single pure tone to each ear separately, listeners may still hear a difference tone . Since the peculiar, non-linear physics of the ear doesn't come into play in this case, it is thought that this must be a separate, neural phenomenon. Compare binaural beats.
Heinz Bohlen proposed what is now known as the Bohlen–Pierce scale on the basis of combination tones, as well as the 833 cents scale.